Mathematical Model Governing the Predator-Prey Relationship in Lake Turkana (Kenya)
- Kingfisher, Pelagic fish, Prey, Predator, Equilibrium points, Stability.
Predator-Prey relationship is a very fundamental aspect of every ecosystem. The associations that exist between different organisms in the ecosystem influence the survival of organisms and the functioning of the ecosystem as a whole. Lake Turkana is an understudied, permanent desert, fresh water lake located in north western, Kenya. Some of the species found in the lake include the Kingfishers and the Palegic fish. In this study the predator-prey relationship between the Kingfishers and the Pelagic fish (Pyrenean minnow) in the Lake Turkana has been analyzed qualitatively. A model of first order differential equations is proposed and studied after making certain simplifying assumptions. The analytical result showed that the system has two equilibriums, namely the trivial equilibrium and the endemic equilibrium which are stable. Numerical simulation was performed and analysis done to show the relationship between the two species. Results obtained from the simulation compares well with data obtained from Turkana Fisheries Company. The changes in the predator-prey species in the lake shows that predation has the balance of nature that exists in this eco-system.